Modern nucleic acid sequencing methods have provided much sequence data and will continue to do so. Analytical methods have led to an increase in understanding in such areas as genetic regulation, dependence of molecular function and structure on sequence, genotypic variability, and molecular evolution and taxonomy. The underlying mathematics of sequence analysis has generally lagged behind the initial biological interpretations, but the mathematical tools have allowed studies of existing inconsistencies and potential limits on some of these initial interpretations. These tools have also had important additional effects such as a rigorous solution of the problem of secondary structure prediction. Primarily these tool are metrics to calculate comparative distances between sequences. It is the potential for continued investigation and application of the fundamental mathematical properties to such large data sets as now exist for biomolecular sequences that underlies this grant work. The investigators will continue the development of comparative sequence methods, the investigation of their detailed properties, and their application to the problems of molecular biology.